Learn QM algebraic formulations and interpretations

Question

I have a good undergrad knowledge of quantum mechanics, and I'm interesting in reading up more about interpretation and in particular things related to how QM emerges algebraically from some reasonable real world assumptions. However I want to avoid the meticulous maths style and rather read something more meant for physicists (where rigorous proofs aren't needed and things are well-behaved ;) ) I.e. I'd prefer more intuitive resources as opposed to the rigorous texts.

Can you recommend some reading to get started?

Answer 1

An excellent book which does more or less what you ask for is Asher Peres' "Quantum theory:concepts and methods". It starts from the Stern-Gerlach experiments and logical reasoning to develop the basic principles of quantum mechanics. From there, it develops the necessary algebra.

Another interesting book for an approach of the conceptual side of quantum mechanics is "Quantum Paradoxes" by Aharonov and Rohrlich. But to fully appreciate this one, I think you will need to go through a standard curriculum first.

Then, there is "Quantum computation and Quantum Information" by Nielsen and Chuang, which is meant as an introduction to the ideas of QM as applied to information theory for people with an informatics background mostly. So it also starts from an algebraic and conceptual approach.

Answer 2

Anthony Sudbery, Quantum Mechanics.... is an excellent text which emphasises the theory and interpretation rather than the drill problems...in fact he is a mathematician and quantum information theorist and this book is not so useful for someone who needs to bone up on their perturbation theory and get ready for QED, it focuses on what it sounds like you are especially interested in.

Answer 3

For matrix mechanics (mixed with a bit of schrodinger), see the NPTEL Lectures.

For path integrals, see Feynman, Hibbs (and Styer) Quantum Mechanics and Path Integrals.

Answer 4

My book

• A. Neumaier and D. Westra, Algebraic Quantum Physics, Vol. 1: Quantum mechanics via Lie algebras, de Gruyter, Berlin 2024.

features a first principle account of quantum mechanics from the point of view of symmetries. The formalism of quantum mechanics is derived in Part II (Chapters 4-6) from the analysis of polarization of classical light (leading to density operators) and the following principle:

Detector response principle (DRP): A detection element $k$ responds to an incident stationary source with density operator $ρ$ with a nonnegative mean rate $p_k$ depending linearly on $ρ$. The mean rates sum to the intensity of the source. Each $p_k$ is positive for at least one density operator $ρ$.

The book is scheduled to appear in paper form on October 7, 2024. Already now, Google books offers a number of free pages, including among others the table of contents and the introductory chapter with an overview over the whole book.

Answer 5

Physical theories are usually understood by working out the consequences of the relevant equations of motion in the same way as for any other scientific theory. This tends to lead to the conclusion that the systems you see around you exist in multiple versions that are roughly sorted into layers each of which evolves approximately like the universe as described by classical physics because of decoherence: the Everett interpretation.

There is a book by David Wallace called "The Emergent Multiverse: Quantum Theory According To The Everett Interpretation" and he has papers about the Everett interpretation such as

https://arxiv.org/abs/1111.2189

There are some lectures about quantum computation using the Everett interpretation that has some material you might find interesting:

https://www.youtube.com/watch?v=mpkYPEaifUg&list=PLqdVnC7OWuEcfKRZXsrooK_EPzwmWSi-N

and some papers about Everettian quantum theory in the Heisenberg picture

https://arxiv.org/abs/quant-ph/0104033

https://arxiv.org/abs/2008.02328

For introductions to quantum field theory that don't say much about interpretations see "Quantum field theory in a nutshell" by Zee and "Quantum field theory for the gifted amateur" by Lancaster and Blundell. For a deeper book about the concepts involved in quantum field theory see "The conceptual framework of quantum field theory" by Anthony Duncan.